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Inventing a Solution vs. Studying a Worked Solution: Which Better Prepares Students for Learning?

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Inventing a Solution vs. Studying a Worked Solution: Which Better Prepares Students for Learning?

By Gordon Eldridge, TIE Columnist

05/24/2017

A previous article I reviewed here (Schwartz et al. 2011) suggested that inventing a solution prepares students well for subsequent direct instruction. The experiment had one group of students invent the solution to a problem involving three contrasting cases while a second group was taught how to solve similar problems, then given the same problem.

The invent-a-solution group showed deeper understanding and greater transfer. But was the positive learning effect due to the process of inventing the solution? Or was it simply that inventing the solution caused students to compare the cases more thoroughly and thus enabled them to notice the deeper structure of the concept?

Researchers from the University of Freiburg in Germany decided to try to get behind this question. They designed experiments comparing the act of inventing a solution with that of studying a worked solution that has been designed specifically to facilitate the kind of comparing and contrasting that seemingly supported learning in the Schwartz et al. experiment.

Study 1

Forty-two student teachers were assigned to two conditions: inventing a solution and studying a worked solution. They were given excerpts from student learning journals containing reflections that illustrated student application of a particular learning strategy. The invent-a-solution group had to devise a set of criteria that could be used to evaluate student application of the strategy. The worked solution group received the evaluations of a fictitious teacher and the criteria used by the teacher. Both groups later received instruction via a computer-based learning environment on the criteria and their application.

What were the results?

• Directly after the preparation task, the inventing group showed higher awareness of knowledge gaps.

• The more knowledge gaps perceived, the more time spent on relevant learning sections in the computer-based learning environment.

• The inventing group showed higher interest in assessment of learning strategies.

• Despite the inventing group’s higher awareness of knowledge gaps and higher levels of interest, the worked solution group achieved better learning outcomes on a post-test.

• The more a participant in the inventing group failed to invent an appropriate solution, the worse the post-test result.

Study 2

Study 2, involving 40 eighth-grade students, broadly replicated the Schwartz et al. study for the invent condition. Three case studies were used; the context involved companies sending clowns to parties and squeezing different numbers of clowns onto buses of various sizes. Students in this condition had to invent a crowdedness index.

The worked solution group was given the same case studies, but with a solution created by a fictitious student. This group was also prompted to self-explain the steps in the worked solution to encourage processing of examples and comparison between the cases.

Both groups were then given a lecture on ratio followed by a post-test with three types of tasks. One involved simple calculation. The second, a near transfer task, required students to create a density index, but with a different cover story. The third, a far transfer task, required students to invent a new kind of index, this time for the stiffness of trampoline fabrics.

What were the results?

The two groups did not differ in level of interest. Directly after the preparation task:

• the inventing group showed higher awareness of knowledge gaps.

• the worked solution group reported higher feelings of self-efficacy.

• the groups did not differ in their understanding of the deep structure of ratio, probably indicating both contrasted cases and paid attention to the critical features.

• on the post-test, both groups gave similar amounts of transfer-relevant information.

However, the inventing group included more surface features, which were irrelevant to the deep structure and therefore to transfer.

• the more a participant in the inventing group failed to invent an appropriate solution, the worse the post-test result.

The Schwartz et al. study and the student teacher study found that inventing led to higher levels of interest and motivation. Why might this not have been the case for the eighth-grade students? In both studies, the inventing group developed a higher awareness of knowledge gaps. Further, in Study 1, perception of knowledge gaps led to more time spent learning relevant material, and this time correlated with positive learning outcomes. The correlation between knowledge gaps and learning for eighth-grade students was negative, however. These apparent discrepancies may yield some useful lessons.

1. Motivation – One possible cause for the eighth-grade students’ unexpected lack of interest may be their lack of prior knowledge in physics and prior skills in problem-solving; as such, collaboration may have been insufficient to benefit from the inventing activity. Evidence that they found the inventing activity overwhelming comes from two sources. Firstly, only 28 percent of the students successfully invented an index (as opposed to 80 percent in the Schwartz study). Secondly, analysis of questionnaires indicated that students who did not find a solution felt less self-efficacious and exhibited lower levels of interest. This may indicate that if students are presented with an overly daunting and unscaffolded challenge, the cost to feelings of self-efficacy may outweigh any potential benefits from exploration.

2. Knowledge gaps – The eighth-grade students seemed unable to take advantage of the knowledge gaps they identified. Perhaps they lacked the metacognitive skills that would have allowed this. Alternatively, the lecture format of direct instruction may not have encouraged self-regulated learning in the same way as the computer-based learning environment in Study

3. If we provide activities with opportunities to identify knowledge gaps, we must both support students in making use of that awareness and ensure that follow-up learning activities allow space for this.

Finally, what might explain the seeming general superiority of worked examples? The researchers suggest that while inventing solutions may generate motivation and support identification of knowledge gaps, worked solutions may prepare students differently for future learning. Worked solutions seem to support learners in developing a level of basic knowledge that is organized in more useful ways. Evidence for this is threefold.

Firstly, the finding that failure to invent an appropriate solution led to less learning suggests that, in both conditions, it was the learners who noticed the critical features of the concept who were successful. Further, research on the continued influence effect suggests that learners who invented suboptimal solutions may have clung to their original, possibly incomplete, or incorrectly organized thinking during the instruction phase and this may have blocked them from noticing the critical features of the concept.

Secondly, evidence of higher extraneous cognitive load in the inventing group may suggest that learners had less working memory available to process relevant details. Finally, while eighth-grade students in both groups were able to understand the deep structure equally, the students in the inventing group remembered significantly more irrelevant surface details, suggesting less “prioritization” of knowledge. Facilitating higher-quality early knowledge in our classrooms requires us to be aware of what students are noticing and not noticing during learning activities. We need to know when students generate sub-optimal solutions, or focus on surface features, so we can provide experiences that directly challenge this thinking. If we cannot create such cognitive conflict, some students may hold onto incomplete conceptions or misconceptions.

Discrepancies aside, two positive takeaways seem to be that, no matter what pedagogical approach we take, comparing and contrasting may be a critical part of supporting students to recognize and understand the deep structure of a concept and that it is understanding this deep structure that facilitates transfer.